Finite Group Databasebeta

← #7615081

Subgroups — #7615081

Order 512.

1692 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59862C211yesmaximal, characteristic, complemented
2#59424C211yesmaximal, characteristic, complemented
3#32620C211yesmaximal, characteristic, complemented
4#32614C211yesmaximal, characteristic, complemented
5#31926C211yesmaximal, characteristic, complemented
6#31917C211yesmaximal, characteristic, complemented
7#28742C211yesmaximal, characteristic, complemented
8#28276C211yesmaximal, characteristic, complemented
9#28123C211yesmaximal, characteristic, complemented
10#28120C211yesmaximal, characteristic, complemented
11#28029C211yesmaximal, characteristic, complemented
12#28017C211yesmaximal, characteristic, complemented
13#27933C211yesmaximal, characteristic, complemented
14#27217C211yesmaximal, characteristic, complemented
15#27208C211yesmaximal, characteristic, complemented
16#27093C211yesmaximal, characteristic, complemented
17#27090C211yesmaximal, characteristic, complemented
18#26263C211yesmaximal, characteristic, complemented
19#26262C211yesmaximal, characteristic, complemented
20#25781C211yesmaximal, characteristic
21#24530C211yesmaximal, characteristic, complemented
22#24527C211yesmaximal, characteristic, complemented
23#24479C211yesmaximal, characteristic, complemented
24#24477C211yesmaximal, characteristic, complemented
25#23189C211yesmaximal, characteristic, complemented
26#22817C211yesmaximal, characteristic, complemented
27#22609C211yesmaximal, characteristic, complemented
28#22436C211yesmaximal, characteristic
29#21599C211yesmaximal, characteristic, complemented
30#21527C211yesmaximal, characteristic, complemented
31C2×#1972C211yesmaximal, characteristic
32C23×D8C2211yescharacteristic
33C2×#495C2211yescharacteristic
34C2×#495C2211yescharacteristic
35C2×#484C2211yescharacteristic
36C2×#483C2211yescharacteristic
37C2×#467C2211yescharacteristic
38C2×#450C2211yescharacteristic
39C2×#450C2211yescharacteristic
40C2×#446C2211yescharacteristic, complemented
41C2×#442C2211yescharacteristic
42C2×#442C2211yescharacteristic
43C2×#441C2211yescharacteristic, complemented
44C22×#106C2211yescharacteristic
45C22×#102C2211yescharacteristic
46C22×#102C2211yescharacteristic
47C22×#97C2211yescharacteristic
48#2796—21no—
49#2786—21no—
50#2751—21no—
51#2740—21no—
52#2601—21no—
53#2595—21no—
54#2592C2211yescharacteristic, complemented
55#2592C2211yescharacteristic, complemented
56#2580C2211yescharacteristic, complemented
57#2561—21no—
58#2560—21no—
59#2538C2211yescharacteristic, complemented
60#2516—21no—
61#2513C2211yescharacteristic, complemented
62#2513C2211yescharacteristic, complemented
63#2512C2211yescharacteristic, complemented
64#2512C2211yescharacteristic, complemented
65#2503C2211yescharacteristic
66#2502C2211yescharacteristic
67#2483—21no—
68#2482—21no—
69#2480—21no—
70#2480—21no—
71#2448C2211yescharacteristic, complemented
72#2448C2211yescharacteristic, complemented
73#2447C2211yescharacteristic, complemented
74#2447C2211yescharacteristic, complemented
75#2437—21no—
76#2435C2211yescharacteristic
77#2435C2211yescharacteristic
78#2367C2211yescharacteristic, complemented
79#2367C2211yescharacteristic, complemented
80#2357C2211yescharacteristic, complemented
81#2354C2211yescharacteristic, complemented
82#2345C2211yescharacteristic
83#2344C2211yescharacteristic
84#2342—21no—
85#2342—21no—
86D4×C22⋊C4C2211yescharacteristic
87D4×C22⋊C4C2211yescharacteristic
88C4×C22⋊Q8C2211yescharacteristic
89C4×C22⋊Q8C2211yescharacteristic
90C4×C22⋊Q8C2211yescharacteristic
91C2×#390C2211yescharacteristic
92C2×#390C2211yescharacteristic
93#2097C2211yescharacteristic, complemented
94#2097C2211yescharacteristic, complemented
95#2096C2211yescharacteristic, complemented
96#2096C2211yescharacteristic, complemented
97#2073C2211yescharacteristic, complemented
98#2073C2211yescharacteristic, complemented
99#2071C2211yescharacteristic, complemented
100#2071C2211yescharacteristic, complemented
101#2067C2211yescharacteristic, complemented
102#2067C2211yescharacteristic, complemented
103#2067C2211yescharacteristic, complemented
104#2067C2211yescharacteristic, complemented
105#2065C2211yescharacteristic, complemented
106#2065C2211yescharacteristic, complemented
107#2065C2211yescharacteristic, complemented
108#2065C2211yescharacteristic, complemented
109#2055C2211yescharacteristic, complemented
110#2055C2211yescharacteristic, complemented
111#2055C2211yescharacteristic, complemented
112#2055C2211yescharacteristic, complemented
113#2055C2211yescharacteristic, complemented
114#2055C2211yescharacteristic, complemented
115#2055C2211yescharacteristic, complemented
116#2055C2211yescharacteristic, complemented
117#2042C2211yescharacteristic, complemented
118#2042C2211yescharacteristic, complemented
119#2042C2211yescharacteristic, complemented
120#2042C2211yescharacteristic, complemented
121#2012C2211yescharacteristic
122#2012C2211yescharacteristic
123#2012C2211yescharacteristic
124#2012C2211yescharacteristic
125#1985C2211yescharacteristic, complemented
126#1983C2211yescharacteristic, complemented
127#1983C2211yescharacteristic, complemented
128#1983C2211yescharacteristic, complemented
129#1983C2211yescharacteristic, complemented
130#1972C2211yescharacteristic
131#1972C2211yescharacteristic
132#1972C2211yescharacteristic
133#1972C2211yescharacteristic
134#1972C2211yescharacteristic
135#1972C2211yescharacteristic
136#1972C2211yescharacteristic
137#1972C2211yescharacteristic
138#1972C2211yescharacteristic
139#1972C2211yescharacteristic
140#1971C2211yescharacteristic, complemented
141#1971C2211yescharacteristic, complemented
142#1971C2211yescharacteristic, complemented
143#1970C2211yescharacteristic
144#1970C2211yescharacteristic
145#1943C2211yescharacteristic, complemented
146#1941C2211yescharacteristic, complemented
147#1941C2211yescharacteristic, complemented
148#1940C2211yescharacteristic, complemented
149#1935C2211yescharacteristic, complemented
150#1935C2211yescharacteristic, complemented
151#1926C2211yescharacteristic, complemented
152#1926C2211yescharacteristic, complemented
153#1926C2211yescharacteristic, complemented
154#1926C2211yescharacteristic, complemented
155#1925C2211yescharacteristic, complemented
156#1925C2211yescharacteristic, complemented
157#1925C2211yescharacteristic, complemented
158#1925C2211yescharacteristic, complemented
159#1920C2211yescharacteristic, complemented
160#1920C2211yescharacteristic, complemented
161#1919C2211yescharacteristic, complemented
162#1919C2211yescharacteristic, complemented
163#1917C2211yescharacteristic, complemented
164#1917C2211yescharacteristic, complemented
165#1892C2211yescharacteristic
166#1892C2211yescharacteristic
167#1880C2211yescharacteristic, complemented
168#1880C2211yescharacteristic, complemented
169#1880C2211yescharacteristic, complemented
170#1880C2211yescharacteristic, complemented
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic
173#1879C2211yescharacteristic
174#1879C2211yescharacteristic
175#1877C2211yescharacteristic, complemented
176#1877C2211yescharacteristic, complemented
177#1877C2211yescharacteristic, complemented
178#1877C2211yescharacteristic, complemented
179#1850C2211yescharacteristic
180#1850C2211yescharacteristic
181#1847C2211yescharacteristic, complemented
182#1847C2211yescharacteristic, complemented
183#1824C2211yescharacteristic
184#1823C2211yescharacteristic
185#1807C2211yescharacteristic
186#1804C2211yescharacteristic, complemented
187#1804C2211yescharacteristic, complemented
188#1802C2211yescharacteristic, complemented
189#1802C2211yescharacteristic, complemented
190#1797C2211yescharacteristic
191#1786C2211yescharacteristic
192#1786C2211yescharacteristic
193#1776C2211yescharacteristic, complemented
194C4×#106C2211yescharacteristic, complemented
195C4×#106C2211yescharacteristic, complemented
196#1771C2211yescharacteristic, complemented
197#1771C2211yescharacteristic, complemented
198#1770C2211yescharacteristic, complemented
199#1763C2211yescharacteristic, complemented
200#1763C2211yescharacteristic, complemented
201#1752C2211yescharacteristic
202C8×C22⋊C4C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×D8—24no—
211C22×D8—24no—
212C22×D8—42no—
213C22×D8C2311yescharacteristic
214C22×D8C2311yescharacteristic
215C22×D8C2311yescharacteristic
216C22×D8C2311yescharacteristic
217C23×C8C2311yescharacteristic
218C23×C8C2311yescharacteristic
219C2×#126—21no—
220C2×#126—21no—
221C2×#124C2311yescharacteristic
222C2×#124C2311yescharacteristic
223C2×#124C2311yescharacteristic
224C2×#124C2311yescharacteristic
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8D411yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×#117—21no—
237C2×#117—21no—
238C22×C4⋊C4C2311yescharacteristic
239C22×C4⋊C4C2311yescharacteristic
240C22×C22⋊C4—21no—
241C22×C22⋊C4—21no—
242C22×C22⋊C4—21no—
243C22×C22⋊C4—21no—
244C22×C22⋊C4—21no—
245C22×C22⋊C4—21no—
246C22×C42C2311yescharacteristic
247#495—24no—
248#495—42no—
249#484—42no—
250#483—42no—
251#467—24no—
252#450—42no—
253#450—42no—
254#446—42no—
255#442—24no—
256#442—42no—
257#441—42no—
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#106—24no—
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#102—42no—
287C2×#102—42no—
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×#97—42no—
311C2×#97C2311yescharacteristic
312C2×#97C2311yescharacteristic
313C2×#97C2311yescharacteristic
314C2×#97C2311yescharacteristic
315C2×#97C2311yescharacteristic
316C2×#97C2311yescharacteristic
317C2×C4×C8C2311yescharacteristic
318C2×C4×C8C2311yescharacteristic
319#400—21no—
320#400—21no—
321#399—21no—
322#399—21no—
323#399—21no—
324#398—21no—
325#398—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#396—21no—
341#396—21no—
342#396—21no—
343#396—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#393—21no—
349#393—21no—
350#393—21no—
351#391D411yescharacteristic
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#390—21no—
359#390—21no—
360#390—21no—
361#390—21no—
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#389D411yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387D411yescharacteristic
414#387D411yescharacteristic
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385D411yescharacteristic
430#385D411yescharacteristic
431#384C2311yescharacteristic
432#384C2311yescharacteristic
433#382C2311yescharacteristic
434#382C2311yescharacteristic
435#381—21no—
436#381—21no—
437#381—21no—
438#381—21no—
439#381—21no—
440#381—21no—
441#380—21no—
442#380—21no—
443#380—21no—
444#380D411yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#379—21no—
448#379—21no—
449#379—21no—
450#379—21no—
451#379—21no—
452#379—21no—
453C4×C4⋊C4—21no—
454C4×C4⋊C4—21no—
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C22⋊C4—21no—
465C4×C22⋊C4—21no—
466C4×C22⋊C4—21no—
467C4×C22⋊C4—21no—
468C4×C22⋊C4—21no—
469C4×C22⋊C4—21no—
470C4×C22⋊C4C2311yescharacteristic
471C4×C22⋊C4C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C25—21no—
498C22×Q8C2×D411yescharacteristic
499C22×Q8C2411yescharacteristic
500C22×Q8C2411yescharacteristic
501C22×D4—22no—
502C22×D4—22no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—22no—
506C22×D4—22no—
507C22×D4—22no—
508C22×D4—22no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4C2411yescharacteristic
516C22×D4C2411yescharacteristic
517C22×D4C2411yescharacteristic
518C22×D4C2411yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4C2×D411yescharacteristic
526C23×C4C2×D411yescharacteristic
527C23×C4C2411yescharacteristic
528C2×Q16—22no—
529C2×Q16—22no—
530C2×Q16—22no—
531C2×SD16—22no—
532C2×SD16—22no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×D8—22no—
544C2×D8—22no—
545C2×D8—22no—
546C2×D8—22no—
547C2×D8—22no—
548C2×D8—22no—
549C2×D8—22no—
550C2×D8—22no—
551C2×D8—22no—
552C2×D8—416no—
553C2×D8—41no—
554C2×D8—41no—
555C2×D8#4114yes—
556C22×C8—22no—
557C22×C8—22no—
558C22×C8—22no—
559C22×C8—41no—
560C22×C8—41no—
561C22×C8#4114yes—
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570#126—82no—
571#126—82no—
572#124—22no—
573#124—22no—
574#124—41no—
575#124—41no—
576#124—41no—
577#124—41no—
578#124—41no—
579#124—41no—
580C22⋊Q8—22no—
581C22⋊Q8—22no—
582C22⋊Q8—22no—
583C22⋊Q8—22no—
584C22⋊Q8—42no—
585C22⋊Q8—82no—
586C4×Q8—41no—
587C4×Q8—41no—
588C4×Q8—41no—
589C4×Q8—41no—
590C4×Q8—41no—
591C4×Q8—41no—
592C4×D4—22no—
593C4×D4—22no—
594C4×D4—41no—
595C4×D4—41no—
596C4×D4—41no—
597C4×D4—41no—
598C4×D4—41no—
599C4×D4—41no—
600#117—82no—
601#117—82no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—22no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2×D411yescharacteristic
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—44no—
690C2×C22⋊C4—44no—
691C2×C22⋊C4—82no—
692C2×C22⋊C4—82no—
693C2×C22⋊C4—82no—
694C2×C22⋊C4—82no—
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C42—21no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—41no—
708C2×C42—41no—
709C2×C42C2×D411yescharacteristic
710C2×C42C2×D411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717#107—22no—
718#107—41no—
719#107—41no—
720#106—22no—
721#106—22no—
722#106—22no—
723#106—22no—
724#106—22no—
725#106—22no—
726#106—41no—
727#106—41no—
728C4⋊C8—41no—
729C4⋊C8—41no—
730C4⋊C8—41no—
731C4⋊C8—41no—
732C4⋊C8—41no—
733C4⋊C8—41no—
734#103—22no—
735#103—22no—
736#103—41no—
737#103—41no—
738#103—41no—
739#103—41no—
740#103—41no—
741#103—41no—
742#103—41no—
743#103—41no—
744#102—22no—
745#102—22no—
746#102—41no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763#102—41no—
764C22⋊C8—22no—
765C22⋊C8—22no—
766#97—22no—
767#97—22no—
768#97—22no—
769#97—22no—
770#97—41no—
771#97—41no—
772C4×C8—22no—
773C4×C8—22no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814C24—21no—
815C24—21no—
816C24—21no—
817C24—21no—
818C24—42no—
819C24—42no—
820C24—42no—
821C24—42no—
822C24—42no—
823C24—42no—
824C24—42no—
825C24—42no—
826C24—81no—
827C24—81no—
828C24—81no—
829C24—81no—
830C24—81no—
831C24—81no—
832C24C22×D411yescharacteristic
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—41no—
846C2×Q8—41no—
847C2×Q8—41no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—82no—
879C2×D4—82no—
880C2×D4—82no—
881C2×D4—82no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4C2×#4112yes—
885C2×D4C2×#4112yes—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—22no—
891C22×C4—22no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—41no—
905C22×C4—41no—
906C22×C4—41no—
907C22×C4—41no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—81no—
917C22×C4—81no—
918C22×C4—81no—
919C22×C4—81no—
920C22×C4—81no—
921C22×C4—81no—
922C22×C4—81no—
923C22×C4—81no—
924C22×C4—81no—
925C22×C4—81no—
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C2×#4112yes—
940C22×C4H(5,𝔽2)12yes—
941C22×C4C2511yescharacteristic
942Q16—44no—
943SD16—82no—
944SD16—82no—
945SD16—82no—
946SD16—82no—
947D8—28no—
948D8—44no—
949D8—44no—
950D8—44no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—28no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—44no—
973C2×C8C2×#4112yes—
974C2×C8C2×#4112yes—
975C2×C8C2×#4112yes—
976C2×C8H(5,𝔽2)12yes—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—41no—
998C4⋊C4—41no—
999C4⋊C4—41no—
1000C4⋊C4—41no—
1001C4⋊C4—41no—
1002C4⋊C4—41no—
1003C4⋊C4—41no—
1004C4⋊C4—41no—
1005C4⋊C4—41no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C22⋊C4—22no—
1023C22⋊C4—22no—
1024C22⋊C4—22no—
1025C22⋊C4—22no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C42—21no—
1075C42—21no—
1076C42—21no—
1077C42—21no—
1078C42—21no—
1079C42—21no—
1080C42—21no—
1081C42—21no—
1082C42—21no—
1083C42—21no—
1084C42—21no—
1085C42—21no—
1086C42—41no—
1087C42—41no—
1088C42—42no—
1089C42—81no—
1090C42—81no—
1091C42—81no—
1092C42—81no—
1093C42—81no—
1094C42—81no—
1095C42—81no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—22no—
1101C23—22no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—84no—
1129C23—84no—
1130C23—84no—
1131C23—84no—
1132C23—84no—
1133C23—84no—
1134C23—84no—
1135C23—84no—
1136C23—162no—
1137C23—162no—
1138C23—162no—
1139C23—162no—
1140C23—162no—
1141C23—162no—
1142C23#55012yes—
1143C23#57512yes—
1144C23#57712yes—
1145C23C23×D411yescharacteristic
1146Q8—41no—
1147Q8—41no—
1148Q8—41no—
1149Q8—41no—
1150Q8—41no—
1151Q8—41no—
1152Q8—41no—
1153Q8—41no—
1154Q8—82no—
1155D4—22no—
1156D4—22no—
1157D4—22no—
1158D4—22no—
1159D4—41no—
1160D4—41no—
1161D4—41no—
1162D4—41no—
1163D4—41no—
1164D4—41no—
1165D4—41no—
1166D4—41no—
1167D4—41no—
1168D4—41no—
1169D4—41no—
1170D4—41no—
1171D4—84no—
1172D4—84no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—82no—
1252C2×C4—82no—
1253C2×C4—84no—
1254C2×C4—84no—
1255C2×C4—162no—
1256C2×C4—162no—
1257C2×C4—162no—
1258C2×C4—162no—
1259C2×C4#55012yes—
1260C2×C4C22×#4111yescharacteristic
1261C2×C4C22×#4111yescharacteristic
1262C2×C4C2×H(5,𝔽2)11yescharacteristic
1263C2×C4C2×H(5,𝔽2)11yescharacteristic
1264C2×C4#58511yescharacteristic
1265C2×C4#58511yescharacteristic
1266C8—22no—
1267C8—41no—
1268C8—41no—
1269C8—41no—
1270C8—41no—
1271C8—41no—
1272C8—41no—
1273C8#55114yes—
1274C22—22no—
1275C22—22no—
1276C22—22no—
1277C22—22no—
1278C22—22no—
1279C22—22no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—168no—
1309C22—168no—
1310C22#340114yes—
1311C22C2×#55011yescharacteristic
1312C22D4×#4111yescharacteristic
1313C22#349611yescharacteristic
1314C22C2×#57511yescharacteristic
1315C22C2×#57711yescharacteristic
1316C22#358511yescharacteristic
1317C22#358511yescharacteristic
1318C4—22no—
1319C4—41no—
1320C4—41no—
1321C4—41no—
1322C4—41no—
1323C4—41no—
1324C4—41no—
1325C4—41no—
1326C4—41no—
1327C4—41no—
1328C4—41no—
1329C4—41no—
1330C4—41no—
1331C4—81no—
1332C4—81no—
1333C4—81no—
1334C4—81no—
1335C4—81no—
1336C4—81no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C4C2×#55111yescharacteristic
1344C4#351011yescharacteristic
1345C4#351311yescharacteristic
1346C4#354211yescharacteristic
1347C2—24no—
1348C2—82no—
1349C2—82no—
1350C2—161no—
1351C2—161no—
1352C2#5982011yescharacteristic
1353C2C2×#340111yescharacteristic
1354C2#6141711yescharacteristic
1355C2#6145411yescharacteristic
1356C2#6152211yescharacteristic
1357C2#6230111yescharacteristic
1358C2#6231911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D8C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #59862C2semidirect
2. #59424C2semidirect
3. #32620C2semidirect
4. #32614C2semidirect
5. #31926C2semidirect
6. #31917C2semidirect
7. #28742C2semidirect
8. #28276C2semidirect
9. #28123C2semidirect
10. #28120C2semidirect
11. #28029C2semidirect
12. #28017C2semidirect
13. #27933C2semidirect
14. #27217C2semidirect
15. #27208C2semidirect
16. #27093C2semidirect
17. #27090C2semidirect
18. #26263C2semidirect
19. #26262C2semidirect
21. #24530C2semidirect
22. #24527C2semidirect
23. #24479C2semidirect
24. #24477C2semidirect
25. #23189C2semidirect
26. #22817C2semidirect
27. #22609C2semidirect
29. #21599C2semidirect
30. #21527C2semidirect
40. C2×#446C22semidirect
43. C2×#441C22semidirect
54. #2592C22semidirect
55. #2592C22semidirect
56. #2580C22semidirect
59. #2538C22semidirect
61. #2513C22semidirect
62. #2513C22semidirect
63. #2512C22semidirect
64. #2512C22semidirect
71. #2448C22semidirect
72. #2448C22semidirect
73. #2447C22semidirect
74. #2447C22semidirect
78. #2367C22semidirect
79. #2367C22semidirect
80. #2357C22semidirect
81. #2354C22semidirect
93. #2097C22semidirect
94. #2097C22semidirect
95. #2096C22semidirect
96. #2096C22semidirect
97. #2073C22semidirect
98. #2073C22semidirect
99. #2071C22semidirect
100. #2071C22semidirect
101. #2067C22semidirect
102. #2067C22semidirect
103. #2067C22semidirect
104. #2067C22semidirect
105. #2065C22semidirect
106. #2065C22semidirect
107. #2065C22semidirect
108. #2065C22semidirect
109. #2055C22semidirect
110. #2055C22semidirect
111. #2055C22semidirect
112. #2055C22semidirect
113. #2055C22semidirect
114. #2055C22semidirect
115. #2055C22semidirect
116. #2055C22semidirect
117. #2042C22semidirect
118. #2042C22semidirect
119. #2042C22semidirect
120. #2042C22semidirect
125. #1985C22semidirect
126. #1983C22semidirect
127. #1983C22semidirect
128. #1983C22semidirect
129. #1983C22semidirect
140. #1971C22semidirect
141. #1971C22semidirect
142. #1971C22semidirect
145. #1943C22semidirect
146. #1941C22semidirect
147. #1941C22semidirect
148. #1940C22semidirect
149. #1935C22semidirect
150. #1935C22semidirect
151. #1926C22semidirect
152. #1926C22semidirect
153. #1926C22semidirect
154. #1926C22semidirect
155. #1925C22semidirect
156. #1925C22semidirect
157. #1925C22semidirect
158. #1925C22semidirect
159. #1920C22semidirect
160. #1920C22semidirect
161. #1919C22semidirect
162. #1919C22semidirect
163. #1917C22semidirect
164. #1917C22semidirect
167. #1880C22semidirect
168. #1880C22semidirect
169. #1880C22semidirect
170. #1880C22semidirect
175. #1877C22semidirect
176. #1877C22semidirect
177. #1877C22semidirect
178. #1877C22semidirect
181. #1847C22semidirect
182. #1847C22semidirect
186. #1804C22semidirect
187. #1804C22semidirect
188. #1802C22semidirect
189. #1802C22semidirect
193. #1776C22semidirect
194. C4×#106C22semidirect
195. C4×#106C22semidirect
196. #1771C22semidirect
197. #1771C22semidirect
198. #1770C22semidirect
199. #1763C22semidirect
200. #1763C22semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#598622
#594242
#326202
#326142
#319262
#319172
#287422
#282762
#281232
#281202
#280292
#280172
#279332
#272172
#272082
#270932
#270902
#262632
#262622
#257812
#245302
#245272
#244792
#244772
#231892
#228172
#226092
#224362
#215992
#215272
C2×#19722